(you might have to click on the image again, when the new tab opens up to see it in better quality)

this was supposed to be my 00-LEDoff circuit because the two switches are set to off and 0 represents off. however the LED lights up! Its an AND gate so its supposed to light up when both switches are turned on. I hope u guys got my problem.

This is what my 01-LEDoff circuit looked like (it also shows what pin does what)

This is what my 10-LEDoff circuit looked like

and this is supposed to the 11-LEDon circuit, but it doesn't light up!

Your problems are due to not having your inputs properly pulled up or tied to ground. A floating input will rise to the operating point of the logic and cause oscillations. It's even possible for these oscillations to overheat and destroy the chip. For TTL, the pull-up resistors should be 4.7K. Just about any other logic family can use larger resistances of 20K.

To work right, your switches should switch to ground. The inputs should be pulled up to Vcc as above.